Due to the strong anisotropic property of the advanced metal materials used in automobile, aviation, and aerospace, experimental flow stress–strain relations including different stress states are necessary to provide the information of anisotropic hardening and plastic flow for constructing a constitutive model. Therefore, reasonably reproducing the experimental stress–strain relations is the most fundamental work to substitute adequate flow stress–strain curves into the constitutive equation at the same time. However, accurate and stable regression results are difficult to obtain through the current regression models such as power exponent, second-order function model, fourth-order function model, and so forth. In this paper, an optimized model named as a least square quadratic regression model (ordinary least square model) was proposed based on the most useful second-order function model. The significant difference is that all experimental points are used to reproduce the experimental stress–strain relations in ordinary least square model in place of only three experimental points adopted in second-order function model, which results in good regression accuracy. Through comparison, it is found that the regression results by power function are poor with regard to some experimental results, and the results reproduced by second-order function model or fourth-order function model are very sensitive to the experimental points selected to do the regression. The sum of squares for error (SSE) increases sharply when the selected points are unreasonable. In addition, for second-order function and fourth-order function models, only limited experimental points are adopted to do the regression, the best regression accuracy cannot be obtained even if the selected points are reasonable. In contrast, SSE of the regression curve by ordinary least square model reduces to less than 50% of the best regressed result by second-order function model, the yielding behavior and variable strain increment ratio of the anisotropic materials can be reflected more accurately. This is very important for accurately describing the plastic flow behaviors of anisotropic materials.
A method for assessing the fit of a constitutive material model to experimental stress–strain data
